Edexcel A-Level Physics: Materials

A small steel ball-bearing is released from rest just below the surface of a tall column of glycerine, a clear, very viscous liquid. The ball sinks, and after a short distance it falls at a constant (terminal) velocity for the rest of its descent.

Explain, in terms of the forces acting on the ball-bearing, why the ball first accelerates and then reaches a constant terminal velocity. In your answer you should name the three forces acting and refer to how each changes as the ball speeds up.

(6 marks)

A rectangular block of softwood is placed in a tank of fresh water and floats with its top face horizontal. The block and the water have the following properties.

Quantity	Value
Length of block	0.30 m
Width of block	0.20 m
Height of block	0.15 m
Density of softwood, $\rho_b$ρb​	700 kg m⁻³
Density of water, $\rho_w$ρw​	1000 kg m⁻³
Gravitational field strength, $g$g	9.81 m s⁻²

(a) Calculate the mass of the block. (2 marks)

(b) Calculate the fraction of the block's volume that is submerged below the water surface. (2 marks)

(c) Calculate the upthrust acting on the floating block. (2 marks)

A student has two identical springs, each obeying Hooke's law. The student connects them together in two different ways — arrangement P and arrangement Q — and records the extension of each arrangement for a range of loads. The results are shown below.

Force / N	Extension of P / m	Extension of Q / m
0	0	0
5	0.10	0.40
10	0.20	0.80
15	0.30	1.20

(a) Use the data to determine the effective spring constant of arrangement P and of arrangement Q. (2 marks)

(b) State, with a reason, which arrangement has the springs connected in series and which has them connected in parallel. (2 marks)

(c) Hence determine the spring constant of a single one of the springs. (1 mark)

A toy catapult uses an elastic cord that obeys Hooke's law with a spring constant of 200 N m⁻¹. A child pulls the cord back so that it is extended by 0.15 m, then releases a small stone of mass 0.040 kg, which is launched horizontally. Assume the stone leaves the catapult at the moment the cord returns to its natural length.

(a) Calculate the elastic strain energy stored in the cord just before release. (2 marks)

(b) Assuming all of this strain energy is transferred to the kinetic energy of the stone, calculate the launch speed of the stone. (2 marks)

(c) State one reason why the actual launch speed would be less than the value calculated in part (b). (1 mark)

A steel wire of diameter 2.0 mm is used to suspend a load from a ceiling. A box of mass 80 kg hangs in equilibrium from the lower end of the wire. The breaking stress of the steel is $5.0 \times 10^{8} \ \text{Pa}$5.0×108 Pa. Take $g = 9.81 \ \text{m s}^{-2}$g=9.81 m s−2.

(a) Calculate the tensile stress in the wire when it supports the 80 kg box. (2 marks)

(b) Deduce whether the wire will break, and calculate the maximum mass the wire could support before reaching its breaking stress. (2 marks)

A metal wire is stretched by an increasing tensile force.

(a) Define the tensile stress and the tensile strain in the wire, giving an equation for each. (2 marks)

(b) State Hooke's law as it applies to the wire. (1 mark)